Asymptotic behavior of exchange ratio in exchange Monte Carlo method

The exchange Monte Carlo (EMC) algorithm is well known as being an improvement on the Markov Chain Monte Carlo method. Although it has been shown to be effective in many different contexts, the mathematical foundation of the EMC method has not yet been established. In this paper, we derive the asymptotic behavior of the symmetrized Kullback divergence and the exchange ratio, which is the acceptance ratio of the exchange process for the EMC method. In addition, based on these derived results, we propose optimal settings for the EMC method.